Does installing/running Blender tamper in any way with my system/settings or install additional software/required components?
No it doesn't modify your system, provided you are using the self-contained .zip version.

The self-contained .zip version is just that, self-contained. It will - of course - put data where-ever you tell it to. Animation output or other temporary files will be written where you tell Blender to put them. Temporary files (in C:\tmp\ by default) are deleted every so often.

In addition to the outputs mentioned above, the Blender Windows Installer will also make a link in you start menu, (possibly) on you desktop and will associate .blend files with the Blender executable. This file association is done via the registry but should be harmless.